I personally know several people who opened up us bank accounts (BofA, Wells Fargo) for their non resident llc.@mickey that is exactly what I have seen too. BUT we have forum users around here at OffshoreCorpTalk that claim it is well possible to travel to the USA walk into a bank with your KYC documents AND your incorporation documents for the company and open an account.
So far there have only be doubtful reports back here that it actually works.
Do you want to elaborate a little more, I get a little confused about what you mean.. not your fault my fault.
call up customer service of the bank and talk to them and they will also confirm that they have no issues with opening account for non residents, it just the first meeting needs to be held in person where the bank officer will read you your rights and the rules as well as tick their boxes for KYC procedures etc.